Re: [EM] Deterministic Epsilon Consensus Idea stimulated by a question of Steve Bosworth
Note that if epsilon is one, the method is just Range Voting on a scale of
zero to five ... which gives a clear incentive for concentrating ratings to
the extremes of zero and five, or the extremes of "reject" and "excellent"
in the MJ terminology.
On the other hand, if epsilon were infinitesimal, the grades above "poor"
would serve merely as tie breakers ... not a bad idea for a general purpose
tie breaker method!
But as a stand alone method, it might be best to limit the choice of
epsilon to a value between zero and 1/6.
Why 1/6? Because of the six levels of grades, a five-sixths majority is a
reasonable partial consensus quota. In particular, an initial step that
disqualified every alternative pairwise defeated by more than a five-sixths
majority of the ballots could never disqualify all candidates when there
are only six levels.
[In general, if there are only k levels, there cannot be a beat cycle where
all of the winning votes consist of fractions greater than (1 - 1/k) of the
ballots.]
This and other considerations make me think that in general when there are
k levels of approval, 1/k might be a good nominal value for epsilon.
This "method" is still in the brainstorming stage, so all suggestions are
worth considering!
El mié., 6 de oct. de 2021 7:38 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:
Steve's query about Chiastic Approval included the following ....
Also, correct me if I'm mistaken that XA does not guarantee that its
winner will be elected with the support of a majority of all the votes
(ballots) cast.
The short answer is "no" ... no method can guarantee majority voter
support for its winner, unless they can guarantee that at least one
candidate is ranked, rated, scored, or graded above bottom on more than
half of the ballots submitted.
The long answer is, "Why stop at half or two-thirds, as some methods
require ... why not go for full 100% consensus?"
But, you may object, full consensus is not always possible. Well, neither
is forty percent support always possible, but that doesn't stop the
Constitution from requiring two-thirds of the voters' support for certain
kinds of amendments, etc.
One expedient that has been suggested is the NOTA option for the case when
the quota is not met. This option gives new meaning to the word "approval"
... as Mike Ossipoff used to say, you approve a candidate if you would
rather see her elected than have to come back next month to vote for
someone else.
I would like to suggest another option based on the standard MJ grade
ballot ...
Each candidate X gets a score that is given by the sum ..
S(X) = Sum (over j from zero to five) of the product
a(j)*epsilon^j,
where epsilon is a value to be determined by the voters ... and the
respective values of a(j), for j in {0, 1, 2, 3, 4} are the number of
ballots on which candidate X is graded strictly above reject, poor,
acceptable, good, or very good, respectively.
Also each voter has the option of voting for a value of epsilon in the set
{.01, .02, ... .99, 1.00}. The median of the distribution of these votes
determines the value of epsilon.
Elect the candidate X with the max value of S(X) (once the epsilon value
has been determined).
Note that if, for some j, the coefficient a(j) is the total number of
ballots, then we can say candidate X is a full consensus candidate at level
j.
If there are several full consensus level j candidates, then the higher
degree terms will determine the winner.
Thanks!
FWS
TO: Forest
FROM: Steve
Currently, I understand your pursuit of the optimal "Epsilon" to be an interesting mathematical challenge for you. However, I do not yet see it as having the prospect of improving the use MJ. Partly, my question follows from you previously agreeing that voting using grades is more meaningful than using numbers. You answered: "Yes, I fully agree on that point; nobody I know likes it when the nurse asks how much it hurts on a scale of one to ten!"
If so, the highest median-grade of any MJ election must be either Excellent, Very Good, Good, Acceptable, Poor, or Reject. How could an election benefit from replacing these judgments with numbers?
In any case, what portion of the electorate is going to understand an explanation of a new voting system that includes one of your phrases below like: "... the winning votes consist of fractions greater than (1 - 1/k) of the ballots."
I look forward to our dialogue.
Steve
From: Forest Simmons forest.simmons21@gmail.com
Sent: Thursday, October 7, 2021 3:50 PM
To: steve bosworth stevebosworth@hotmail.com
Cc: EM Election-methods@lists.electorama.com
Subject: Re: Deterministic Epsilon Consensus Idea stimulated by a question of Steve Bosworth
Note that if epsilon is one, the method is just Range Voting on a scale of zero to five ... which gives a clear incentive for concentrating ratings to the extremes of zero and five, or the extremes of "reject" and "excellent" in the MJ terminology.
On the other hand, if epsilon were infinitesimal, the grades above "poor" would serve merely as tie breakers ... not a bad idea for a general purpose tie breaker method!
But as a stand alone method, it might be best to limit the choice of epsilon to a value between zero and 1/6.
Why 1/6? Because of the six levels of grades, a five-sixths majority is a reasonable partial consensus quota. In particular, an initial step that disqualified every alternative pairwise defeated by more than a five-sixths majority of the ballots could never disqualify all candidates when there are only six levels.
[In general, if there are only k levels, there cannot be a beat cycle where all of the winning votes consist of fractions greater than (1 - 1/k) of the ballots.]
This and other considerations make me think that in general when there are k levels of approval, 1/k might be a good nominal value for epsilon.
This "method" is still in the brainstorming stage, so all suggestions are worth considering!
El mié., 6 de oct. de 2021 7:38 p. m., Forest Simmons <forest.simmons21@gmail.commailto:forest.simmons21@gmail.com> escribió:
Steve's query about Chiastic Approval included the following ....
Also, correct me if I'm mistaken that XA does not guarantee that its winner will be elected with the support of a majority of all the votes (ballots) cast.
The short answer is "no" ... no method can guarantee majority voter support for its winner, unless they can guarantee that at least one candidate is ranked, rated, scored, or graded above bottom on more than half of the ballots submitted.
The long answer is, "Why stop at half or two-thirds, as some methods require ... why not go for full 100% consensus?"
But, you may object, full consensus is not always possible. Well, neither is forty percent support always possible, but that doesn't stop the Constitution from requiring two-thirds of the voters' support for certain kinds of amendments, etc.
One expedient that has been suggested is the NOTA option for the case when the quota is not met. This option gives new meaning to the word "approval" ... as Mike Ossipoff used to say, you approve a candidate if you would rather see her elected than have to come back next month to vote for someone else.
I would like to suggest another option based on the standard MJ grade ballot ...
Each candidate X gets a score that is given by the sum ..
S(X) = Sum (over j from zero to five) of the product
a(j)*epsilon^j,
where epsilon is a value to be determined by the voters ... and the respective values of a(j), for j in {0, 1, 2, 3, 4} are the number of ballots on which candidate X is graded strictly above reject, poor, acceptable, good, or very good, respectively.
Also each voter has the option of voting for a value of epsilon in the set {.01, .02, ... .99, 1.00}. The median of the distribution of these votes determines the value of epsilon.
Elect the candidate X with the max value of S(X) (once the epsilon value has been determined).
Note that if, for some j, the coefficient a(j) is the total number of ballots, then we can say candidate X is a full consensus candidate at level j.
If there are several full consensus level j candidates, then the higher degree terms will determine the winner.
Thanks!
FWS
The verbiage is intended for developers, not users. Programmers have to
convert everything to numbers via ASCII codes, etc. All of this must be out
of sight to keep the users from pointless worry. The design stage is for
the EM scientists to work out the nitty gritty details. Yes, it's fun for
us, but it is also necessary... for us, but not for Joe Q Public. You are
not a programmer, but you are a promoter, so you need to know more than the
user, but not as much as a software engineer. Does that help?
El jue., 7 de oct. de 2021 7:58 p. m., steve bosworth <
stevebosworth@hotmail.com> escribió:
TO: Forest
FROM: Steve
Currently, I understand your pursuit of the optimal "Epsilon" to be an
interesting mathematical challenge for you. However, I do not yet see it as
having the prospect of improving the use MJ. Partly, my question follows
from you previously agreeing that voting using grades is more meaningful
than using numbers. You answered: "Yes, I fully agree on that point; nobody
I know likes it when the nurse asks how much it hurts on a scale of one to
ten!"
If so, the highest median-grade of any MJ election must be either
Excellent, Very Good, Good, Acceptable, Poor, or Reject. How could an
election benefit from replacing these judgments with numbers?
In any case, what portion of the electorate is going to understand an
explanation of a new voting system that includes one of your phrases below
like: "... the winning votes consist of fractions greater than (1 - 1/k) of
the ballots."
I look forward to our dialogue.
Steve
From: Forest Simmons forest.simmons21@gmail.com
Sent: Thursday, October 7, 2021 3:50 PM
To: steve bosworth stevebosworth@hotmail.com
Cc: EM Election-methods@lists.electorama.com
Subject: Re: Deterministic Epsilon Consensus Idea stimulated by a
question of Steve Bosworth
Note that if epsilon is one, the method is just Range Voting on a scale of
zero to five ... which gives a clear incentive for concentrating ratings to
the extremes of zero and five, or the extremes of "reject" and "excellent"
in the MJ terminology.
On the other hand, if epsilon were infinitesimal, the grades above "poor"
would serve merely as tie breakers ... not a bad idea for a general purpose
tie breaker method!
But as a stand alone method, it might be best to limit the choice of
epsilon to a value between zero and 1/6.
Why 1/6? Because of the six levels of grades, a five-sixths majority is a
reasonable partial consensus quota. In particular, an initial step that
disqualified every alternative pairwise defeated by more than a five-sixths
majority of the ballots could never disqualify all candidates when there
are only six levels.
[In general, if there are only k levels, there cannot be a beat cycle
where all of the winning votes consist of fractions greater than (1 - 1/k)
of the ballots.]
This and other considerations make me think that in general when there are
k levels of approval, 1/k might be a good nominal value for epsilon.
This "method" is still in the brainstorming stage, so all suggestions are
worth considering!
El mié., 6 de oct. de 2021 7:38 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:
Steve's query about Chiastic Approval included the following ....
Also, correct me if I'm mistaken that XA does not guarantee that its
winner will be elected with the support of a majority of all the votes
(ballots) cast.
The short answer is "no" ... no method can guarantee majority voter
support for its winner, unless they can guarantee that at least one
candidate is ranked, rated, scored, or graded above bottom on more than
half of the ballots submitted.
The long answer is, "Why stop at half or two-thirds, as some methods
require ... why not go for full 100% consensus?"
But, you may object, full consensus is not always possible. Well, neither
is forty percent support always possible, but that doesn't stop the
Constitution from requiring two-thirds of the voters' support for certain
kinds of amendments, etc.
One expedient that has been suggested is the NOTA option for the case when
the quota is not met. This option gives new meaning to the word "approval"
... as Mike Ossipoff used to say, you approve a candidate if you would
rather see her elected than have to come back next month to vote for
someone else.
I would like to suggest another option based on the standard MJ grade
ballot ...
Each candidate X gets a score that is given by the sum ..
S(X) = Sum (over j from zero to five) of the product
a(j)*epsilon^j,
where epsilon is a value to be determined by the voters ... and the
respective values of a(j), for j in {0, 1, 2, 3, 4} are the number of
ballots on which candidate X is graded strictly above reject, poor,
acceptable, good, or very good, respectively.
Also each voter has the option of voting for a value of epsilon in the set
{.01, .02, ... .99, 1.00}. The median of the distribution of these votes
determines the value of epsilon.
Elect the candidate X with the max value of S(X) (once the epsilon value
has been determined).
Note that if, for some j, the coefficient a(j) is the total number of
ballots, then we can say candidate X is a full consensus candidate at level
j.
If there are several full consensus level j candidates, then the higher
degree terms will determine the winner.
Thanks!
FWS
On 08.10.2021 07:25, Forest Simmons wrote:
The verbiage is intended for developers, not users. Programmers have to
convert everything to numbers via ASCII codes, etc. All of this must be
out of sight to keep the users from pointless worry. The design stage is
for the EM scientists to work out the nitty gritty details. Yes, it's
fun for us, but it is also necessary... for us, but not for Joe Q
Public. You are not a programmer, but you are a promoter, so you need to
know more than the user, but not as much as a software engineer. Does
that help?
Let me try to make what might be Steve's implicit argument a little
stronger.
With MJ, it's true that if you want to assign numerical values to the
grades, the exact numbers you use don't matter as long as they're
monotone in the grades themselves: the number assigned to Poor should be
less than the number assigned to Acceptable, and so on.
Is that true of the epsilon method? If not, it requires more information
than MJ. If I recall correctly, by B&L's model, the grades are not
supposed to exist on any given numerical scale, but the society that
uses MJ should have a common idea of what "Excellent" means relative to
"Poor".
I have only cursorily read the method proposal, but you said:
Note that if epsilon is one, the method is just Range Voting on a
scale of zero to five ... which gives a clear incentive for
concentrating ratings to the extremes of zero and five, or the extremes
of "reject" and "excellent" in the MJ terminology.
That suggests that the epsilon method has a more demanding
interpretation of the grades - that a common language of what
"Excellent" means is not enough, since it implicitly assigns each grade
a definite score if epsilon happens to be chosen to be one.
-km
Good points! Evidently I misunderstood what Steve was getting at. In that
light I'm embarrassed to say that my reply seems quite condescending.Thanks
for restoring to Steve the credit that he deserves!
That said, if the naive voter can vote a sincere ballot solely on the basis
of the commonly understood meanings of the descriptions excellent(ideal),
very good, good, acceptable, poor, and reject .... then that ballot can be
used equally well for MJ, Super MJ, and Epsilon Consensus, whether for
macro or micro values of epsilon.
If epsilon is positive but less than 1/N^6, where N is the number of
ballots, then the order of scores for the respective alternatives is the
lexicographical order of 6-tuples of the form (a0, a1, a2, a3, a4, a5)
where the alpha numerics a0, a1, a2, a3, a4, and a5 represent the
respective numbers of ballots on which the alternative under consideration
is graded better than or equal to reject, poor, acceptable, good, very
good, or excellent, respectively.
My original intention for Epsilon Consensus was as a tie breaker (with
infinitesimal epsilon) for Super Majority Judgment ... but it is much
simpler to just allow epsilon to assume standard (but appropriately small)
values to supply a stand-alone method.
As long as epsilon is small enough, this method gives no more incentive for
grade inflation than MJ does, which its proponents aver to be more or less
negligible, depending on the voter levels of naïveté.
The contemplated Super MJ is no easier or harder than MJ, but if the voters
will vote sincerely, i.e. with the same naivete as MJ voters (thereby
producing identical ballot sets for both MJ&SMJ) super majority
alternatives will be more favored under SMJ talley rules, which makes a
higher degree of consensus likely for SMJ:
For a given alternative j and grade g in the ordered set [reject, ...,
excellent], let F(j, g) be the number of ballots on which alternative j is
graded at or better than g.
Note that for every j, the ballot number F(j, reject) has the same value N,
the total number of ballots submitted.
Let g(j) be the max value of g such that F(j, g) is greater than or equal
to (5/6)N.
The SMJ winner is chosen from argmax g(j) by use of any previously agreed
upon tie breaker method ... I suggest Epsilon Consensus with the value of
epsilon set at 1/N^6 .
FWS
El vie., 8 de oct. de 2021 12:46 p. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:
On 08.10.2021 07:25, Forest Simmons wrote:
The verbiage is intended for developers, not users. Programmers have to
convert everything to numbers via ASCII codes, etc. All of this must be
out of sight to keep the users from pointless worry. The design stage is
for the EM scientists to work out the nitty gritty details. Yes, it's
fun for us, but it is also necessary... for us, but not for Joe Q
Public. You are not a programmer, but you are a promoter, so you need to
know more than the user, but not as much as a software engineer. Does
that help?
Let me try to make what might be Steve's implicit argument a little
stronger.
With MJ, it's true that if you want to assign numerical values to the
grades, the exact numbers you use don't matter as long as they're
monotone in the grades themselves: the number assigned to Poor should be
less than the number assigned to Acceptable, and so on.
Is that true of the epsilon method? If not, it requires more information
than MJ. If I recall correctly, by B&L's model, the grades are not
supposed to exist on any given numerical scale, but the society that
uses MJ should have a common idea of what "Excellent" means relative to
"Poor".
I have only cursorily read the method proposal, but you said:
Note that if epsilon is one, the method is just Range Voting on a
scale of zero to five ... which gives a clear incentive for
concentrating ratings to the extremes of zero and five, or the extremes
of "reject" and "excellent" in the MJ terminology.
That suggests that the epsilon method has a more demanding
interpretation of the grades - that a common language of what
"Excellent" means is not enough, since it implicitly assigns each grade
a definite score if epsilon happens to be chosen to be one.
-km